Theoretical analysis of the stability problem for the control systems with distributed parameters shall be given. The approach to the analysis of such systems can be composed of two parts. First, the distributed parameter element is modeled by a frequency response function. Second, approximate conditions of parametric resonance are derived by a method of stationarization (describing functions of time-variant elements). The approach is illustrated by two examples. One is a robot-manipulator arm (distributed mechanical parameter system) controlled by a controller with a modulator/demodulator cascade (time-varying element). Another is an electromechanical transformer that consists of a constant current motor and a synchronous generator. Inductance between stator windings and the rotor of the synchronous generator serves as a periodical time-varying parameter, and a long electrical line plays the role of an element with distributed parameters. In both examples, dangerous (in terms of the first parametric resonance) regions for time-varying parameter are obtained theoretically and compared with simulation experiment.
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Conditions of Parametric Resonance in Periodically Time-Variant Systems With Distributed Parameters
Yong-Kwan Lee,
Yong-Kwan Lee
Senior Researcher
Central R&D Institute,
e-mail: lurpy@hanmail.net
SAMSUNG Electro-Mechanics Co.
, Maetan 3-Dong, Suwon, Gyungi-Do 443-743, Republic of Korea
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Leonid S. Chechurin
Leonid S. Chechurin
Head
Department of Innovation Theory,
e-mail: cepreu4@gmail.com
St. Petersburg State Polytechnic University
, 195251 Polytechnicheskaya str., 29 St. Petersburg Russia
Search for other works by this author on:
Yong-Kwan Lee
Senior Researcher
Central R&D Institute,
SAMSUNG Electro-Mechanics Co.
, Maetan 3-Dong, Suwon, Gyungi-Do 443-743, Republic of Koreae-mail: lurpy@hanmail.net
Leonid S. Chechurin
Head
Department of Innovation Theory,
St. Petersburg State Polytechnic University
, 195251 Polytechnicheskaya str., 29 St. Petersburg Russiae-mail: cepreu4@gmail.com
J. Dyn. Sys., Meas., Control. May 2009, 131(3): 031008 (11 pages)
Published Online: March 20, 2009
Article history
Received:
November 6, 2007
Revised:
November 8, 2008
Published:
March 20, 2009
Citation
Lee, Y., and Chechurin, L. S. (March 20, 2009). "Conditions of Parametric Resonance in Periodically Time-Variant Systems With Distributed Parameters." ASME. J. Dyn. Sys., Meas., Control. May 2009; 131(3): 031008. https://doi.org/10.1115/1.3072151
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